Solving Ordinary Differential Equations. - Volume 1, Nonstiff Problems, 2nd Revised Edition

The subject of the book is the solution of nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory from Newton, Leibniz, Euler and Hamilton to limit cycles and strange attractors. In a second chapter a modern treatment of Runge-Kutta and extrapolation methods is given. Also included are continuous methods for dense output, parallel Runge-Kutta methods, special methods for Hamiltonian systems, second order differential equations and delay equations. The third chapter begins with the classical theory of multistep methods, treats variable step size and Nordsieck methods, and concludes with the theory of general linear methods. Many applications from physics, chemistry, biology and astronomy together with computer programs and numerical comparisons are presented. For this second edition many sections have been rewritten and new material included.